https://en.wikipedia.org/wiki/Public_housing_in_Singapore
This is pretty much the exact opposite of the nationalize-all-the-things public housing concept, which presumably is why it's not devolved into the usual electoral capture/tragedy of the commons sh show
If you're not married, you can't get public housing until you're 35.
If you do qualify, you have to enter a lottery for the opportunity to choose a unit. The chances of winning the first time are low.
Then once you've won, the wait time is 4-5 years before you actually get the place. But people do it because you can buy the unit subsidized, then after ~5 years, you can sell it at market rates. It's basically a free hand out by the governement.
For example, my Googling seems to suggest that you could buy a 4BR in a new neighbourhood for under 350k. A new estate in Melbourne would be double that, with no public transport or other amenities.
It's worth noting that Singapore's average household income is around 1/5th that of Australia.
A quick Google shows an average household income of $116k AUD for Aussies, and $114k SGD for (resident) Singaporeans. Current exchange rates peg 1 SGD to 0.997 AUD.
Singapore solved this (and other issues) by creating a department that basically functions as the nation's largest property developer.
https://en.wikipedia.org/wiki/Housing_and_Development_Board
Net result is about 80% of residents living in public housing.
https://en.wikipedia.org/wiki/Public_housing_in_Singapore